This invention provides a means of holding and supporting rod or tube stock while it is held and rotated by a collet or chuck during machining. Such rod and tube stock, at least initially, is of substantial length and may not have a center line which, lengthwise of the stock, is an unvarying straight line. Thus, the portion of the stock which extends rearwardly from the collet or chuck can be caused to flex radially during rotation. Even if the centerline of the stock is straight, high speed rotation can initiate lateral flexing which, once started, can be caused to increase in intensity. This has resulted in some products machined from the stock being out of tolerance and, therefore, unacceptable. The flexing or whipping of the tail end of the stock causes serious and excessive wear of the equipment. Further, it is hazardous. To avoid this situation, a significant portion of the rod or tube stock frequently has not been used or was used in another process or became scrap and was returned for remelt. This has been a particularly vexing and expensive problem contributing materially to the cost of the acceptable parts which have been produced.